The objective of this application is to develop new statistical models and methods to analyze longitudinal medical cost data, e.g., monthly or other medical cost data collected over time. Compared to the analysis of total cost data which discards a great amount of information, the availability of longitudinal cost data can make health economic analyses more efficient and interpretation more comprehensive, insightful, and useful. We first propose a longitudinal four-part model, with four joint equations modeling respectively: (1) the probability of seeking medical treatment, (2) the probability of being hospitalized, and the actual amount of (3) outpatient and (4) inpatient costs. Our model simultaneously takes account of the inter-temporal correlation of each patient and the cross-equation correlation of the four equations, by joint generalized linear mixed models (GLMM) for binary outcome in (1) and (2), and linear mixed models for log transformed cost in (3) and (4); To circumvent the re-transformation issue in log transformed cost, we next propose a two part random effects model with a Gamma GLMM in part II for the amount of positive cost. Furthermore, we also consider a more flexible generalized Gamma distribution for the amount of positive cost. [unreadable] [unreadable] In Aim 3 we introduce a two-part random effects model for longitudinal medical costs, with proportional hazards model in the second part. An appealing feature of the proportional hazards model is that the baseline hazard is unspecified (nonparametric), accommodating the fact that positive medical cost data are often highly skewed and heteroscedastic, which can not be described by any simple parametric distribution. [unreadable] [unreadable] Our model can be used to ascertain the risk factors of medical costs and identify the most cost-effective treatment. To illustrate this we apply our proposed new model to monthly medical costs of 1,397 chronic heart failure patients from the clinical data repository (CDR) at the University of Virginia. We also compare the results from this model with those from the existing models in terms of consistency and accuracy for generating financial forecasts. [unreadable] [unreadable] Finally, we will develop ready-to-use software to facilitate the application of our methods in practical data analysis. [unreadable] [unreadable] [unreadable]